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Transport Coefficients and nPI Methods

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation and suggests that one can calculate the next-to-leading contribution to transport coefficients from the 4-loop 4PI effective action. The integral equations have been derived for shear viscosity for a scalar theory with cubic and quartic interactions, with a non-vanishing field expectation value. We review these results, and explain how the calculation could be done at higher orders.